Frictional Force Direction Problem

[amitSingh95]

1. Homework Statement

The system is in equilibrium. All the surfaces in the image are rough. The direction of friction on B due to A is :
(a) is upward
(b) is downward
(c) is zero
(d) depends on the masses of A and B.
ANS : (a)

Homework Equations

M_Ag = 2μN (Friction due to wall and due to B)
N=F

The Attempt at a Solution

Since the gravitational force is balanced by the frictional force on A by B and the wall, the direction of frictional force due to B and the wall on A must be upward and therefore, direction of force due to A on B must be downward, i.e., (b), but I am not sure that my reasoning is correct and I don't understand why it should be upward?

 

[NTW]

Let's simplify the situation. Sometimes, imagining an extreme helps... You are told that all surfaces are rough, but not necessarily equally rough. Well, let's imagine that the surfaces where A is in contact with the wall are so rough, that it's the same as if A was welded with the wall... Or, we may say that they are so rough that it's very, very much like a weld. That would mean a very, very high (but finite) friction coefficient between the wall and A. The problem becomes more simple, as you are left only with A and B...

 

[HallsofIvy]

There is a force pressing B against A but since that is perpendicular to A's surface, there is no friction force there. There is a force downward due to gravity. If B is not sliding downward, due to A's friction force, then the force must be in the opposite direction, upward.

 

[haruspex]

Since the gravitational force is balanced by the frictional force on A by B and the wall, the direction of frictional force due to B and the wall on A must be upward

At least one of them must be upward, but no reason why both should be.

 

[Chestermiller]

If you do a free body diagram on B, you will see that the weight of B must be balanced by an upward frictional force at the interface with A. These are the only vertical forces acting on B. So A must exert an upward frictional force on B (equal to the weight of B).

Chet

 

[amitSingh95]

Thank you everyone for your reply, I understand that the direction must be upwards to balance the weight of B. The only confusion I have is due to Newton's third law of motion according to which the direction must be in opposite to the force that B is applying on A.

 

[amitSingh95]

At least one of them must be upward, but no reason why both should be.

The tendency of A is to slide down, with respect to both B and the wall, and frictional force acts in direction opposite to the motion or its tendency, at least in this case I think it is, so shouldn't the direction of force due to both be upwards?

 

[NascentOxygen]

The tendency of A is to slide down, with respect to both B

I don't think we can say that.

Block B is not exerting any upwards force on A, rather the weight of B is acting to tend to cause B to slide downwards relative to A. There is no force acting to maintain B in position, save the upwards force delivered by A through friction.

and the wall, and frictional force acts in direction opposite to the motion or its tendency, at least in this case I think it is, so shouldn't the direction of force due to both be upwards?

The wall pushs up on A, and A pushes up on B.

If there was no friction between the wall and A, then the outcome would be that both would free-fall together as one.

 

[haruspex]

The tendency of A is to slide down, with respect to both B and the wall, and frictional force acts in direction opposite to the motion or its tendency, at least in this case I think it is, so shouldn't the direction of force due to both be upwards?

A has a tendency to slide down, called gravity, but it has no particular desire to slide down in relation to any other given object. Since the wall cannot move, it can derive support from the wall, but there is no basis for assuming it will gain support from B, rather than B gaining support from A.

 

[Chestermiller]

Thank you everyone for your reply, I understand that the direction must be upwards to balance the weight of B. The only confusion I have is due to Newton's third law of motion according to which the direction must be in opposite to the force that B is applying on A.

What is it about this that you are finding confusing? A exerts an upward force on B, and B exerts a downward force on A. So...?

Chet

 

[amitSingh95]

What is it about this that you are finding confusing? A exerts an upward force on B, and B exerts a downward force on A. So...?

Chet

I thought B and the wall both were exerting upward force on A to balance its weight, but now I know that the wall alone is balancing its weight.

 

[Chestermiller]

I thought B and the wall both were exerting upward force on A to balance its weight, but now I know that the wall alone is balancing its weight.

Actually, the wall is doing more than just balance the weight of A. It is also supporting the downward force that B is exerting on A. So the wall is balancing the weight of both A and B.

Chet

 

[NascentOxygen]

I thought B and the wall both were exerting upward force on A to balance its weight, but ...

That would/could be true IFF^✻ the force F had a component acting vertically. But in the case under consideration here, F acts perfectly horizontally, so it can't push B upwards.

^✻ IFF ─ is read as "if and only if"

 

[amitSingh95]

Thanks to everyone
I got it :)